Cycle Harder, Pedal Faster, Go Faster, Ride More, Try Intervals
Overall, I think your best options are to enjoy your bike riding, and simply to do it as consistently as possible. Sell all motorized vehicles and rely on bicycles for all your transportation. :)
According to the math connected to this chart your expected calorie burn rate should be about:
- 380 kCals/hour at or under 16 km/h (leisurely)
- 570 kCals/hour between 16 km/h and 19 km/h (typical speed for a bicycle commuter)
- 760 kCals/hour between 19 km/h and 23 kmh (moderate effort, very doable with practice)
- 950 kCals/hour between 23 km/h and 26 km/h (vigorous)
- 1140 kCals/hour between 26 km/h and 31 km/h (very fast)
- 1530 kCals/hour over 31 km/h (racing)
You should be extremely skeptical about such estimates, since the effort to go 20 km/h into a 10 km/h headwind is nearly ten times as much as going 20 km/h with a 10 km/h tailwind. In addition to wind resistance, hills make a ton of difference. It's nearly 0 effort to go down a steep hill and quite a bit of effort to go up it, and you can easily notice a significant difference in effort with slopes you wouldn't even notice as sloping when walking or driving a car. And acceleration is more effort than cruising at a set speed.
The rolling resistance of a bicycle is quite low and doesn't really change as you go faster. The air resistance for going a given distance increases by the square of your speed. So, yes, if you go the same distance and do it faster, you should burn more calories doing it.
Note though that the difference in the calorie burn between that 16 km/h and 19 km/h speed for two hours (380 kCals) is roughly one bagel with a single pat of butter. There's a lot to be said for adjusting your nutrition to reduce your calorie intake, like Ryan and Ivo suggest in the comments.
A bike computer that measures your speed wouldn't hurt; it would give you something to try to increase. One that measures your cadence (pedaling speed) as well as ground-speed would be better. Best would be a heart rate monitor (which some bike computers support talking to) since that's the most practical way to tell how many calories you're burning. (bike computers that actually measure your power output are prohibitively expensive, however).
For calorie burning, it's usually recommended to do intervals. Basically, after you've warmed up: pedal as hard and fast as you can until your legs burn (30-45 seconds), take it easy for a couple minutes, then push hard again. Making a point of sprinting from the stops is a good way to get some of that kind of push in. This will get your heart rate up and generally burn more calories, but will also help increase your leg strength so that you can do better burning more calories as you progress.
As an avid cyclist, I find it hard to figure out how I would do intervals on a singlespeed. When I want to push myself to go faster, I spin up a bit faster, then shift into a higher gear so that I'm still pushing against a decent amount of resistance. Without shifting I'd just spin out and be unable to push myself harder. Rolling hills on a singlespeed would be very similar to intervals, but it sounds like you don't really have those on your route.